Dear Angel, Thank you very much. This indeed seems a simplest way to extract width of particle size distribution (basically, formula 22 of your article; using only pV mixing parameter value).
There are two questions: 1) (purely practical) could anybody suggest a good way to proceed in case of alpha1-alpha2 doublets? Fitting by single peak even at moderately low angles would yield strong bias (in my test, ~10% in eta vales for 2theta in the 30-35deg. range). Alpha2-stripping (using standard methods implemented e.g. in Powder4) inevitably gives artifacts which would not allow to do a further single-peak fit with the desired accuracy. Constrained fits are possible, but rather difficult. If this is indeed a preferred option, can anybody suggest a good software to do such fits? 2) as far as I understand, the lognormal/pV model predicts that pV mixing parameter is independent of 2theta. In case when one observes "really strong" size broadening, small angle-dependent contribution from instrumental broadening can be neglected. So, if such dependence is experimentally observed (for data where instrumental contribution is small), would this mean that there is non-negligible strain (or "non-trivial" size distribution...)? Or I simply misunderstood something? Sincerely, Maxim. -----Original Message----- From: alor...@unex.es [mailto:alor...@unex.es] Sent: Monday, December 08, 2008 11:03 PM To: Максим В. Лобанов Subject: Re: calculation of VWDS and SWDS from distributions? Maxin: If you fit a lognormal function to your distribution of sizes, then you can easily use Eqs.(24) to (27) in my attached paper. Hope this is easier. Best regards, Angel. L. Ortiz > Dear colleagues, > > I am facing a problem of correlating laser scattering (DLS) and X-ray > diffraction data. > For correct comparison, I need either to calculate some model > distribution from X-ray data (this is feasible assuming lognormal > distribution - there are ready software solutions for that) or typical > "X-ray sizes" (Dv and/or > Da) from given distributions. > The inverse task (calculating Dv and/or Da from given distributions) > appears to be very simple, but it seems there is no ready software > solution, and I need to manually integrate the data. But before doing > that I would like just to be sure that I use correct formulae. > I read the paper dealing with that in great detail (JAC, 35, 338 by > Popa & Balzar, Ref. 1), but it is too mathematical, and I am not > completely confident if I understood everything correctly. > > If we denote distribution (normalized to unity) as p(x), x=particle > size then, according to Ref.1: > Dv=3mu_4/2mu_3 (1) > and > Da=4mu_3/3mu_2 (2) > > Do I understand correctly, that moments mu_i are just: > > mu_i=Int[0, Infinity]{x^i*p(x)dx} > > Or there are some missing factors somewhere? > > Sincerely, > Maxim. > > ------------------------------------------- > Dr. Maxim Lobanov > R&D Director > Huntsman-NMG > mailto: m_loba...@huntsman-nmg.com > > ********************************* > If you encounter any difficulties > sending e-mails to the addresses in huntsman-nmg.com domain, this > could be due to the our spam filter malfunction. > In case of such an event please send a message to n...@fromru.com > > Please note that the old domain nmg.com.ru does not exist anymore - > please update your address book accordingly > > >
